Využití teorie grafů v dopravě

Abstract

{In my bachelor thesis, we will use graph theory to design an optimal traffic control of crossroads. Graph theory is a part of discrete mathematics. We can imagine graphs as a simplification of the real world, where our problem is represented by vertices and edges. In this work, we will describe how to convert a given crossroad to a graph, we will well color its vertices afterward. We will describe how to construct a graph and how to graph color properly. We find the chromatic number of the given graph, moreover we will determine the order the traffic should enter the crossroad. We will deal with elimination of collision situations that may occur when passing through the crossroad, and will also demonstrate several general types of crossroads, that can be immediately used to resolve situations, because they are general. In conclusion, we will compare the existing solutions with a procedure which we suggest.